Weak localization in radiative transfer of acoustic waves in a randomly-fluctuating slab

TL;DR

This paper derives radiative transfer equations for acoustic waves in a randomly fluctuating slab, analyzing boundary effects and wave energy transport in the weak-scattering regime.

Contribution

It introduces a novel derivation of radiative transfer equations for acoustic waves in a slab with boundary effects, using an asymptotic analysis of the Wigner transform.

Findings

Boundary effects influence energy density at the slab boundaries.

Constructive interference inside the slab affects the coherent energy density.

Wave scattering modeled effectively in the weak-scattering regime.

Abstract

This paper concerns the derivation of radiative transfer equations for acoustic waves propagating in a randomly fluctuating slab (between two parallel planes) in the weak-scattering regime, and the study of boundary effects through an asymptotic analysis of the Wigner transform of the wave solution. These radiative transfer equations allow to model the transport of wave energy density, taking into account the scattering by random heterogeneities. The approach builds on the method of images, where the slab is extended to a full-space, with a periodic map of mechanical properties and a series of sources located along a periodic pattern. Two types of boundary effects, both on the (small) scale of the wavelength, are observed: one at the boundaries of the slab, and one inside the domain. The former impact the entire energy density (coherent as well as incoherent) and is also observed in half-spaces. The latter, more specific to slabs, corresponds to the constructive interference of waves that have reflected at least twice on the boundaries of the slab and only impacts the coherent part of the energy density.